I understand that this game requires a game code to play online. What about LAN, though? Is it possible to play a LAN multiplayer game on several computers with just one purchase? I would install it on two or three laptops I own to play with friends. Would this work, or would a code for each installed copy be required even for LAN? thanks.

No, as per: http://forums.introversion.co.uk/viewtopic.php?t=11073

GOG / Introversion just lost one sale thanks to this stupid limitation. Who needs money when you've only delayed a pirate for all of 20 minutes? /s